Heisenberg Linear Chain Model Research Articles

Magnetic exchange interactions and non-Debye relaxation in spin-3/2 frustrated Kagomé magnet Co3V2O8

We report the experimental determination of the magnetic exchange parameter ( J/kB = 2.88 ± 0.02 K) for the Spin-3/2 ferromagnetic (FM) Kagomé lattice system: Co3V2O8 using the temperature dependence of dc-magnetic susceptibility χ(T) data by employing the fundamental Heisenberg linear chain model. Our results are quite consistent with the theoretically reported nearest neighbor dominant FM exchange coupling strength Jex−NN∼ 2.45 K. Five different magnetic phase transitions (6.2–11.2 K) and spin-flip transitions (9.6–7.7 kOe) have been probed using the ∂ ( χT )/ ∂T vs. T, heat capacity (CP -T) and differential isothermal magnetization curves. Among such sequence of transitions, the prominent ones being incommensurate antiferromagnetic (AFM) state at 11.2 K, commensurate AFM state at 8.8 K, and commensurate FM state across 6.2 K. All the successive magnetic phase transitions have been mapped onto a single H-T plane through which one can easily distinguish the above-mentioned different phases. The magnetic contribution of the CP -T near TN (11.2 K) has been analyzed using the power-law expression CM = A|T — TN|−α resulting in the critical exponent α = 0.18 ± 0.01 (0.15 ± 0.003) for T < TN (T > TN ), respectively for the Co3V2O8. It is interesting to note that non-Debye type dipole relaxation is quite prominent in Co3V2O8 and was evident from the Kohlrausch–Williams–Watts analysis of complex modulus and impedance spectra (0 ⩽β⩽ 1). Mott’s variable-range hopping of charge carriers process is evident through the resistivity analysis ( ρac -T −1/4 ) in the temperature range 275 ∘C–350 ∘C. Moreover, the frequency-dependent analysis of σac (ω) follows Jonscher’s power law yielding two distinct activation energies ( Ea∼ 0.37 and 2.29 eV) between the temperature range 39 ∘C–99 ∘C and 240 ∘C–321 ∘C.

Determination of the tricritical point, H–T phase diagram and exchange interactions in the antiferromagnet MnTa2O6

Using the analysis of the temperature and magnetic field dependence of the magnetization (M) measured in the temperature range of 1.5 K to 400 K in magnetic fields up to 250 kOe, the magnetic field-temperature (H–T) phase diagram, tricritical point and exchange constants of the antiferromagnetic MnTa2O6 are determined in this work. X-ray diffraction/Rietveld refinement and x-ray photoelectron spectroscopy of the polycrystalline MnTa2O6 sample verified its phase purity. Temperature dependence of the magnetic susceptibility χ (=M/H) yields the Néel temperature T N = 5.97 K determined from the peak in the computed ∂(χT)/∂T vs T plot, in agreement with the T N = 6.00 K determined from the peak in the C P vs T data. The experimental data of C P vs T near T N is fitted to C P = A|T − T N|−α yielding the critical exponent α = 0.10(0.13) for T > T N (T < T N). The χ vs T data for T > 25 K fits well with the modified Curie–Weiss law: χ = χ 0 + C/(T − θ) with χ 0 = −2.12 × 10−4 emu mol−1 Oe−1 yielding θ = −24 K, and C = 4.44 emu K mol−1 Oe−1, the later giving magnetic moment μ = 5.96 μ B per Mn2+ ion. This yields the effective spin S = 5/2 and g = 2.015 for Mn2+, in agreement with g = 2.0155 measured using electron spin resonance spectroscopy. Using the magnitudes of θ and T N and molecular field theory, the antiferromagnetic exchange constants J 0/k B = −1.5 ± 0.2 K and J ⊥/k B = −0.85 ± 0.05 K for Mn2+ ions along the chain c-axis and perpendicular to the c-axis respectively are determined. The χ vs T data when compared to the prediction of a Heisenberg linear chain model provides semiquantitative agreement with the observed variation. The H–T phase diagram is mapped using the M–H isotherms and M–T data at different H yielding the tricritical point T TP (H, T) = (17.0 kOe, 5.69 K) separating the paramagnetic, antiferromagnetic, and spin-flop phases. At 1.5 K, the experimental magnitudes of the exchange field H E = 206.4 kOe and spin-flop field H SF = 23.5 kOe yield the anisotropy field H A = 1.34 kOe. These results for MnTa2O6 are compared with those reported recently in the isostructural MnNb2O6.

Crystal structure and magnetic behavior within a new molecular magnet containing [Ni(dmit)2]− monoanion

ABSTRACTIn this study, a new metal-dithiolene charge transfer salt with a formula of [3,4-Cl,Cl-Bz-1-APy][Ni(dmit)2] (1; 3,4-Cl,Cl-Bz-1-APy = 1-N-(3′,4′-dichlorobenzyl)pyridinium, dmit = l,3-dithiole-2-thione-4,5-dithiolate) was synthesized and characterized. The crystal of 1-Me2CO belongs to triclinic space group P-1, the [Ni(dmit)2]− anions and 3,4-Cl,Cl-Bz-1-APy+ cations form mixed column stacks with alternating anionic (A) and cationic (C) in the …ACAC… fashion, along the crystallographic a-axis direction. The [Ni(dmit)2]− anions formed a uniform one-dimensional chain via lateral-to-lateral S…S contacts. From the view of crystal structure, an uniform S = ½ Heisenberg linear chain model could be chosen for the fits of the temperature dependent magnetic susceptibilities of 1, but the attempt on this fit is failed. The simple Curie-Weiss law was used for the fits of magnetic susceptibility of 1. The fitted Curie constant is larger than the spin-only value expected for an S = ½ system.

Crystal structures, magnetic and dielectric features of two new isostructural one-dimensional platinum-bis-dithiolene molecular solids

Two new one-dimensional (1-D) molecular solids, [CH2=CH-BzPy][Pt(mnt)2] (1) and [CH2=CH-BzPy-d5][Pt(mnt)2] (2) where CH2=CH-BzPy-d5+=1-N-(4-vinylbenzyl) pyridinium-d5 and mnt2−=maleonitriledithiolate, were synthesized and characterized. A structural phase transition undergoes with TC≈335K in the crystals of 1 and 2, which were confirmed by variable-temperature magnetic susceptibility and DSC measurements. Crystals of 1 and 2 are isostructural in both high- and low-temperature phases. Besides the strong similarity in crystal structures, they show quite analogous magnetic and dielectric features. Above TC, the magnetic behavior is failed to follow the S=½ Heisenberg linear chain model; below TC, a spin gap is opened for 1 and 2. The thermally-assisted dielectric relaxation occurs above ca. 280K for 1 and 2, and this relaxation process is related to the dipole motion of the disordered CH2CH groups in the cation under an ac electrical field.

Structural, Magnetic, and Computational Correlations of Some Imidazolo‐Fused 1,2,4‐Benzotriazinyl Radicals

1,3,7,8-Tetraphenyl-4,8-dihydro-1H-imidazolo[4,5g][1,2,4]benzotriazin-4-yl (5), 8-(4-bromophenyl)-1,3,7-triphenyl-4,8-dihydro-1H-imidazolo[4,5g][1,2,4]benzotriazin-4-yl (6), and 8-(4-methoxyphenyl)-1,3,7-triphenyl-4,8-dihydro-1H-imidazolo[4,5g][1,2,4]benzotriazin-4-yl (7) were characterized by using X-ray diffraction crystallography, variable-temperature magnetic susceptibility studies, and DFT calculations. Radicals 5-7 pack in 1 D π stacks made of radical pairs with alternate short and long interplanar distances. The magnetic susceptibility (χ vs. T) of radicals 5 and 6 exhibit broad maxima at (50±2) and (50±4) K, respectively, and are interpreted in terms of an alternating antiferromagnetic Heisenberg linear chain model with average exchange-interaction values of J = -31.3 and -35.4 cm(-1) (gsolid = 2.0030 and 2.0028) and an alternation parameter a = 0.15 and 0.38 for 5 and 6, respectively. However, radical 7 forms 1 D columns of radical pairs with alternating distances; one of the interplanar distances is significantly longer than the other, which decreases the magnetic dimensionality and leads to discrete dimers with a ferromagnetic exchange interaction between the radicals (2J = 23.6 cm(-1) , 2zJ' = -2.8 cm(-1) , gsolid = 2.0028). Magnetic exchange-coupling interactions in 1,2,4-benzotriazinyl radicals are sensitive to the degree of slippage and inter-radical separation, and such subtle changes in structure alter the fine balance between ferro- and antiferromagnetic interactions.

Spin-Peierls transition in genuine organic TCNQ salt with pyrazine-based cation (N-Me-2,5-di-Me-Pz)(TCNQ)2

The magnetic susceptibility measurements in the temperature range from 2 K to 300 K have been performed on a novel genuine organic TCNQ salt (N-Me-2,5-di-Me-Pz)(TCNQ)2. Based on previous study of similiar material spin-ladder like behaviour was expected. However, obtained experimental data are analyzed in terms of the Heisenberg linear chain model. Transition with spin-Peierls features occurs due to the peculiarities of crystalline structure.

Spin-glass behaviour in the coordination polymer [Co(C3H3N2)2

The magnetic behaviour of the coordination polymer [Co(C3H3N2)2]n has been investigated by magnetization and specific heat measurements. Low-field magnetic susceptibility shows the presence of two maxima at approximately 8 and 4 K (Tf), which reflect short-range low-dimensional antiferromagnetic behaviour and the existence of a spin-glass-like state, respectively. The latter state was observed by magnetic irreversibility in both the zero-field cooled and field-cooled data, and was also confirmed by specific heat measurements. The magnetic specific heat (Cmag) shows a lack of any long-range ordered peaks. Instead, a broad maximum near Tf was observed in the Cma)(T)/T-curve. Below Tf, the Cmag(T) data follow the relation: Cmag(T)/T = gamma + AT. We suggest that the competition of the antiferromagnetic (AF) intra-chain and the ferromagnetic (F) inter-chain interactions in a low-dimensional arrangement of magnetic Co2+ ions can produce the spin-glass behaviour in the sample. The susceptibility data was analyzed in terms of a spin S = 3/2 Heisenberg linear-chain model with a small exchange energy and is consistent with the presence of both F and AF interactions. The splitting of the crystal field energy levels of the Co2+ ions causes a Schottky-type specific heat anomaly of around 60 K.

One-dimensional magnetic interaction in BaMn 2Si 2O 7

BaMn 2Si 2O 7 crystallizes in the BaCo 2Si 2O 7 structure type. Its structure has been refined by Rietveld techniques from X-ray powder diffraction data. The magnetic susceptibility ( χ m) and specific heat ( C p) of this compound show a predominant one-dimensional magnetic interaction when T>20°C, which can be understood in the framework of the Heisenberg linear chain model. The magnetic interaction between the chains becomes appreciable at lower temperature. The one-dimensional magnetic interaction corresponds to the quasi-one-dimensional structure of this compound.

Magnetic Properties of 3-(4-R-Phenyl)-1,5-diphenyl-6-oxo- and -thioxoverdazyl Radical Crystals (R = OCH3, CH3, CN, and NO2)

Magnetic susceptibilities of 8 kinds of 3-(4-R-phenyl)-1,5-diphenyl-6-oxo- and -thioxoverdazyl radical crystals (p-MDpOV (R = OCH3), p-MeDpOV (R = CH3), p-CyDpOV (R = CN), p-NDpOV (R = NO2), p-MDpTV (R = OCH3), p-MeDpTV (R = CH3), p-CyDpTV (R = CN), and p-NDpTV (R = NO2)) were measured between 4.2 and 300 K. The susceptibilities of p-MDpOV, p-CyDpOV, and p-MDpTV can be well explained by a one-dimensional (1D) antiferromagnetic (AFM) Heisenberg linear chain model with exchange interaction of 2 J/k = −27.3, −27.3, and −10.9 K, respectively. The susceptibility of p-MeDpTV can be interpreted in terms of a 1D AFM Heisenberg alternating chain model with 2 J1/k = −92.0 K (alternation parameter α = J2/J1 = 0.7). On the other hand, the susceptibilities of p-MeDpOV, p-NDpOV, and p-CyDpTV follow the Curie−Weiss law with positive Weiss constants of +2.5, +1.5, and +2.9 K, respectively, and the exchange interactions 2 J/k were estimated to be +7.0, +5.0, and +7.0 K, assuming the one-dimensionality for these radical cr...

Magnetic properties of a new type of 1,5-diphenyl-6-oxo- and -thioxo-verdazyl radicals

The magnetic susceptibilities of the 3-(4-chlorophenyl)-1,5-diphenyl-6-oxoverdazyl ( p-CD pOV), 3-(4-bromophenyl)-1,5-diphenyl-6-oxoverdazyl ( p-BD pOV), 1,3,5-triphenyl-6-thioxoverdazyl (TTV), and 3-(4-chlorophenyl)-1,5-diphenyl-6-thioxoverdazyl ( p-CD pTV) radicals have been measured between 4.4 and 300 K. The susceptibility of p-CD pOV and p-BD pOV follows the Curie-Weiss law with a positive and negative Weiss constant of +2.5 and −7.7 K, respectively. On the other hand, the susceptibility of TTV and p-CD pTV can be interpreted in terms of an alternating and nonalternating antiferromagnetic Heisenberg linear chain model with an exchange interaction of 2 J 1/ k = −66.0 K (alternation parameter α = J 2/ J 1 = 0.6) and 2 J/ k = −58.5 K, respectively.

Magnetic-properties of 1,4-dihydro-1,2,4-benzotriazin -4-yl radicals

Magnetic susceptibilities of 1,4-dihydro-1,3-diphenyl-1,2,4-benzotriazin-4-yl (DDB 1), 3-tert-butyl-1,4-dihydro-1-phenyl-1,2,4- benzotriazin-4-yl (BDPB 2) and 1-(4-chlorophenyl)-1,4-dihydro-3-phenyl-1,2,4-benzotriazin-4-yl (CDPB 3) radicals have been measured in the temperature range of 4.2-300 K. The susceptibility of DDB 1 and BDPB 2 follows the Curie-Weiss law with a negative Weiss constant of −2.2 and −0.3 K, respectively. The magnetic susceptibility of CDPB 3, on the other hand, exhibits a broad maximum at 138 K. This susceptibility can be interpreted in terms of an alternating antiferromagnetic Heisenberg linear chain model with an exchange interaction of 2 J 1/ k=−220 K and an alternation parameter of α= J 2/ J 1=0.3. The results of the X-ray structure analysis of CDPB 3 support the above explanation.

Relation between Exchange Interaction and Crystal Structure of Verdazyl Radicals. As Studied by Means of McConnell’s Spin Density Hamiltonian

Abstract The exchange interactions in four kinds of verdazyl crystals, 2,4,6-triphenylverdazyl (TPV), 2,4,6-triphenyl-3-methylverdazyl (MeTPV), 2,4,6-tri-p-tolylverdazyl (TTV), and 2,6-di-p-tolyl-4-phenylverdazyl (DTPV), have been studied by means of McConnell’s spin density Hamiltonian. The calculated exchange parameters, J, have been compared with the experimental values derived from the magnetic susceptibilities. The observed order of J’s J⁄k=−5.4 (TPV), −9.1 (MeTPV), −11.1 (DTPV), and 0–−0.3 K (TTV), can be qualitatively explained by the following equation: J∝\undersetijΣ (−1⁄rij)ρilρjl+1, where ρil and ρjl+1 are π-spin densities on atoms i and j of the l-th and (l+1)-th molecules in the crystallographic column and rij is the interatomic distance between atoms i and j. The magnetic susceptibility data of MeTPV and TTV between 1.6 and 300 K are presented and interpreted with the Heisenberg linear chain model. The susceptibility of DTPV is re-interpreted in the same framework as above.

Magnetic Susceptibility and Crystal Structure of 1,5-Diphenyl-3-(4-chlorophenyl)verdazyl Radical

Abstract The magnetic susceptibility of 1,5-diphenyl-3-(4-chlorophenyl)verdazyl (Cl-TPV) has been measured on a powder sample in the temperature region between 1.8 and 80 K. It exhibited a round maximum at 21.0 K; this temperature is the highest among those observed for verdazyl monoradicals. The susceptibility can be well described by the Heisenberg linear chain model; the estimated exchange interaction parameter is J⁄k=−16.4 K. The crystal structure of Cl-TPV has been determined by means of X-ray diffraction. The crystal is orthorhombic, with the space group of Pbca and with a=22.041(5), b=7.166(4), c=21.379(5) Å, and Z=8. The molecules are arranged in a column along the b axis. The exchange interaction has been discussed based on the crystal structure and the spin density distribution.

Specific heat of (C 6H 11NH 3) CuCl 3 (CHAC), a system of ferromagnetic chains

The heat capacity of (C 6H 11NH 3) CuCl 3 (CHAC) has been measured for 0.45 < T < 60 K. Three-dimensional ordering is observed at T = 2.214 K. The data in the paramagnetic region can be described by a ferromagnetic S = 1 2 Heisenberg linear chain model system with J/ k = +45 ± 5K.

Synthesis, magnetic susceptibility, and Moessbauer spectra of iron(III) dimers and iron(II) polymers containing 2,5-dihydroxy-1,4-benzoquinones

Abstract : Several iron complexes of the dianions of 2,5-dihydroxy-1,4-benzoquinone (DHBQ) and 2, 5-dichloro-3,6-dihydroxy-1,4-benzoquinone (CA, chloranilate dianion) have been prepared and studied by magnetic susceptibility and Moessbauer spectroscopic methods. Iron(II) salts react with these dihydroxybenzoquinones to give polymeric Fe(DHBQ)(H2O)2 and Fe(CA)(H2O)2. If the reaction is carried out in the presence of pyrazine, pyr, (Fe(CA)(pyr))(n) and (Fe(DHBQ)(pyr)) are obtained. Infrared spectral results are consistent with the presence of bridging bidentate pyr in these complexes, and thus sheet polymers. Dimeric Fe2(DHBQ)3(H2O)4 and Fe2(CA)3(H2O)4 .4H2O are obtained by reacting FeCl3 with the respective dihydroxybenzoquinones. Magnetic susceptibility vs. temperature data obtained for the polymeric materials are fit to a S=2 Heisenberg linear chain model. The presence of an anisotropy in the recoilless fraction (Goldanskii-Karyagin effect) is observed in the Fe57 Moessbauer spectra of the Fe(III) dimers and is substantiated by measurements on the temperature dependence of the Moessbauer parameters.

Magnetic specific heats of four spin [formula omitted] linear chain compounds of formula MnX 2L 2 ( X = Cl, Br; L = N2C3H4, NC5H5)

The specific heats of the compounds MnX 2L 2 with X = Cl or Br and L = N 2 C 3 H 4 (pyrazole) or NC 5H 5 (pyridine), have been measured in the 1.3–80 K temperature range. The well-resolved broad maxima in the magnetic specific heat curves of all the compounds can be interpreted in terms of linear chain exchange interactions. The measured specific heats are compared with the isotropic antiferromagnetic Heisenberg linear chain model, but a model assuming, in addition, a moderately large single-ion anisotropy gives a much better agreement with experiment. The values obtained for the intrachain exchange parameter are in the range 0.5 K < | J/ k| < 1 K, and for the uniaxial single-ion anisotropy parameter, 0.2 K < | D/ k| < 0.5 K. The lambda-like anomalies observed in MnBr 2.2pz, MnCl 2.2py and MnBr 2.2py at T = 1.930 K, 1.380 K and 2.055 K, respectively, are attributed to long-range ordering due to the influence of weak interchain interactions. The strength of the interchain interactions has been estimated as about 1% of the intrachain interactions. The compound MnCl 2.2pz does not exhibit a transition to a long-range ordered state down to 1.3 K, which suggests that the interactions between the chains are very weak.

Specific heat of hydrazinium-transition metal-sulfate linear chain compounds

Specific-heat data in the temperature range of 1.3 K to 80 K are presented on polymeric M(II)(N 2H 5) 2(SO 4) 2 compounds where M(II) = Cu, Ni, Co, Fe and Mn. Broad maxima in the magnetic specific heat, pointing to magnetic linear chain exchange interactions, are observed. For the Co, Fe and Mn compounds, λ-like anomalies have also been observed which are indicative of the onset of three-dimensional long-range spin ordering. From the specific-heat measurements information is obtained about the anisotropy of the intrachain exchange interaction, single-ion anisotropy and the magnitudes of the intrachain and interchain interaction parameters of these compounds. The results on the Cu and Mn compounds were fitted to the antiferromagnetic Heisenberg linear chain model with spin 1 2 and 5 2 , respectively. Although this model yields reasonable fits, deviations were observed near the maxima of the curves. For the Cu compound this is ascribed to anisotropy in the exchange interactions and for the Mn compound to interchain coupling effects. In order to fit the data on the Ni and Fe compounds it was found necessary to introduce single-ion anisotropy. The results for the Ni compound were fitted to the Ising spin 1 2 linear chain model with in addition a Schottky curve, and to recent calculations for the spin 1 antiferromagnetic Heisenberg linear chain model with in addition uniaxial single-ion anisotropy. The exchange parameter J/k is found to be much smaller than the zero-field splitting parameter D/k, thus giving rise to Ising properties of the spins at low temperatures. The Co compound was found to exhibit anisotropic exchange interactions which are, in contrast to what is generally found for Co 2+, of the planar type. The results were fitted to the spin 1 2 antiferromagnetic XY linear chain model, as calculated by Katsura, with an exchange parameter J/ k = −7.05 K.

Linear-chain antiferromagnetism in compounds Mn X2L2, with X = Cl, Br, and L = pyrazole, pyridine

Antiferromagnetic interactions have been studied in compounds Mn X 2 L 2( X = Cl, Br; L = pyrazole, pyridine) which have a crystal structure containing dihalide-bridged Mn 2+ linear chains. The magnetic susceptibility of the compounds is interpreted on the basis of the antiferromagnetic Heisenberg linear-chain model with spin S = 5 2 . The intrachain interaction parameter J k of the various compounds lies in the region −(0·5–1·0)K. Results of specific heat measurements and paramagnetic line width studies agree reasonably with the susceptibility data. In addition, the ESR line width studies in the temperature region 100–300 K show that | J k | increases with decreasing temperatures. Finally an estimate of the ratio between the inter- and intrachain interaction parameters is given.

ON THE MAGNETIC SUSCEPTIBILITIES OF SOME IMINOXYL RADICALS

Abstract Magnetic susceptibilities of organic stable radicals, derivatives of 2,2,6,6-tetramethyl-4-hydroxypiperidine-1-oxyl (TANOL), have been measured. The magnetic susceptibility of Ethyl-TANOL showing a broad maximum at a temperature of 0.17 K agrees well with the antiferromagnetic Heisenberg linear chain model, while that of Methyl-TANOL exhibits a characteristic feature of the three dimensional antiferromagnet.